Application of fractional order theory of thermoelasticity to a 2D problem for a half-space

• Published in: Applied mathematics and computation Vol. 248; pp. 584 - 592
• Main Authors: Sherief, Hany H., Abd El-Latief, A.M.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.12.2014
• Subjects: 2D thermoelasticity; Computation; Derivatives; Fractional calculus; Generalized thermoelasticity; Half space; Half spaces; Inverse; Mathematical models; Thermoelasticity; Traction; Two dimensional; Half space; 2D thermoelasticity; Fractional calculus; Generalized thermoelasticity
• ISSN: 0096-3003; 1873-5649
• DOI: 10.1016/j.amc.2014.10.019

•A 2D half space problem for the new fractional order theory of thermoelasticity.•Laplace and exponential Fourier transform techniques are used.•The inverse transforms are obtained using a numerical technique.•Predictions of the theory are discussed and compared with older theory. In this work, we apply the fractional order theory of thermoelasticity to a 2D problem for a half-space. The surface of the half-space is taken to be traction free and is subject to heating. There are no body forces or heat sources affecting the medium. Laplace and exponential Fourier transform techniques are used to solve the problem. The inverse Laplace transforms are obtained using a numerical technique. The predictions of the theory are discussed and compared with those for the generalized theory of thermoelasticity. We also study the effect of the fractional derivative parameter on the behavior of the solution. Numerical results are computed and represented graphically for the temperature, displacement and stress distributions.